High-pressure Raman study of two ferroelectric crystals closely related to PbTiO3

We report high-pressure Raman measurements of the zone-center phonons in two ferroelectric crystals that closely resemble the $\mathrm{AB}{\mathrm{O}}_3$ perovskite crystal PbTi${\mathrm{O}}_3$. These crystals are (${\mathrm{Pb}}_{0.22}$ ${\mathrm{Ba}}_{0.78}$)Ti${\mathrm{O}}_3$, i.e., Ba replacing Pb on the $A$ site, and Pb(${\mathrm{Ti}}_{0.81}$ ${\mathrm{Sn}}_{0.19}$)${\mathrm{O}}_3$, i.e., Sn replacing Ti on the $B$ site. In both cases, at room temperature, we follow the modes and determine $P_c$, the transition pressure from the ferroelectric tetragonal phase to the cubic phase, to be 4.3 and 9.0 GPa, respectively. By observing the coalescence to the same frequency of the appropriate high-energy $A_1\left(\mathrm{TO}\right)+E\left(\mathrm{TO}\right)$ pairs of phonons, we determine the second-order character of the phase transitions at $P_c$. The tendency towards a second-order phase transition seems to be the rule at $P_c$ as long as one makes the measurements at a temperature well below $T_c$; this is in agreement with theory. Thus, these systems exhibit tricritical points in the ($P$,$T$) phase diagram. The soft-$E\left(\mathrm{TO}\right)$-phonon frequency (${\omega }_0$) and damping constant ($\gamma$) can be measured to pressures reasonably close to $P_c$ while the mode remains underdamped. These results are discussed in terms of a frequency-independent damping constant for the behavior of ${\omega }_0$ and $\gamma$ near $P_c$. In the (Pb,Ba)Ti${\mathrm{O}}_3$ crystal, the hydrostatic pressure increases the intensity of the soft $A_1\left(\mathrm{TO}\right)$ mode making it observable. This seems to happen in general in the perovskites. In the Pb(Ti,Sn)${\mathrm{O}}_3$ crystal we observe the coupling of the soft $E\left(\mathrm{TO}\right)$ mode with an extra mode at 59 ${\mathrm{cm}}^{-1\mathrm{}}$; this also has been studied as a function of temperature.